GCF of 350/70, 200/9960
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 350/70, 200/9960 i.e 50/69720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 350/70, 200/9960.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 350/70,200/9960?
Given fractions are 350/70,200/9960
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 350/70,200/9960, numerators are 350,200
Denominators are 70,9960
The GCF of 350,200 is 50 .
LCM of 70,9960 is 69720.
The greatest common factor of 350/70,200/9960 = [GCF of 350,200]/[LCM of 70,9960]= 50/69720
Therefore, the GCF of 350/70,200/9960 is 50/69720.
To find the highest common factor of 350,200, we have to find the factors of both numbers and list the highest common factor.
The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
The HCF of 350,200 is 50.
Lets's calculate GCF of 350,200
| 2 | 350, 200 |
| 5 | 175, 100 |
| 5 | 35, 20 |
| 7, 4 |
∴ So the GCF of the given numbers is 2 x 5 x 5 = 50
Greatest Common Factor of 350,200 By Matching Biggest Common Factor Method
Now, list down the factors of 350
:1,2,5,7,10,14,25,35,50,70,175,350
Now, list down the factors of 200
:1,2,4,5,8,10,20,25,40,50,100,200
Greatest Common Factor
We found the factors 350,200 . The biggest common factor number is the GCF number.
So the greatest common factor 350,200 is 50.
Lets's calculate LCM of 70,9960
| 2 | 70, 9960 |
| 5 | 35, 4980 |
| 7, 996 |
∴ So the LCM of the given numbers is 2 x 5 x 7 x 996 = 69720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 50/69720
Therefore, the GCF of Fractions 350/70,200/9960 is 50/69720
Least Common Multiple of 70,9960 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 70,9960 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,9960) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(70,9960) x common factors =10 x 1 = 10
LCM(70,9960) = ( 70 × 9960 ) / 10
LCM(70,9960) = 697200 / 10
LCM(70,9960) = 69720
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FAQs on GCF of Fractions of 350/70, 200/9960
1. What is the HCF of 350,200?
The HCF of 350,200 is 50
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 350/70, 200/9960?
Answer: GCF of Numerators as per given numbers 350/70, 200/9960 is
GCF of Numerators i.e. for 350,200 is 50
LCM of denominators i.e. for 70,9960 is 69720.
Thus, GCF of Fractions is 50/69720.Finally, GCF of Fractions for 350/70, 200/9960 is 50/69720.